TY - JOUR
T1 - The Weak Galerkin Finite Element Method for Solving the Time-Dependent Stokes Flow
AU - Wang , Xiuli
AU - Liu , Yuanyuan
AU - Zhai , Qilong
JO - International Journal of Numerical Analysis and Modeling
VL - 5
SP - 732
EP - 745
PY - 2020
DA - 2020/08
SN - 17
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/17877.html
KW - Stokes problem, weak Galerkin finite element method, discrete weak gradient,
discrete weak divergence.
AB - <p style="text-align: justify;">In this paper, we solve the time-dependent Stokes problem by the weak Galerkin (WG)
finite element method. Full-discrete WG finite element scheme is obtained by applying the implicit
backward Euler method for time discretization. Optimal order error estimates are established for
the corresponding numerical approximation in $H^1$<sup>&nbsp;</sup>norm for the velocity, and $L^2$&nbsp;norm for both
the velocity and the pressure in semi-discrete forms and full-discrete forms, respectively. Some
computational results are presented to demonstrate the accuracy, convergence and efficiency of
the method.</p>